You have heard that in sports like boxing there might be some competitive advantage to those wearing red uniforms. You want to test this with your new favorite sport of chess-boxing. You randomly assign blue and red uniforms to contestants in 20 matches and find that those wearing red won 14 times (or 70%). You conduct a test of significance using simulation and get the null distribution shown. (Note this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) 

a. Suppose you want to see whether competitors wearing red win more than 50% of the matches in the long run, so you test H₀: π = 0.50 versus H_a: π > 0.50. What is your p-value based on the provided null distribution? 

b. Suppose you now want to see whether competitors wearing either red or blue have an advantage, so you test H₀: π = 0.50 versus H_a: π ≠ 0.50. What is your p-value now based on the provided null distribution?

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Probability of success (m): 0.5 Sample size (n): 20 Number of samples: 100 Animate: [ Draw Samples Total = 100 18 12 6 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Proportion of successes